Worked example · GSM8US
A decision-maker's question, the scenario built to answer it, the numbers the model returns, and the brief a client receives. Every figure is from the certified reference experiment in the GSM8US documentation.
Every number is a comparison. The scenario is run, the same economy is run again without the rate change, and the figure reported is the gap between the two in the year named, in percent. A GDP figure of −1.89 percent in year 3 means GDP is 1.89 percent lower in year 3 than it would have been without the tightening. It does not mean GDP fell. Where a number is set by the scenario design rather than solved by the model, the text says so.
The question
If the Federal Reserve holds rates a full percentage point above its projected path for a year, what does that cost the real economy, and how much of the answer depends on whether the Fed reacts to its own consequences or simply holds course?
The kind of question this model is built forThe answer turns on two things. The first is how deep the contraction goes and how much of it comes back. The second is whether the Federal Reserve holds the rate where the scenario puts it or responds to the inflation and employment its own tightening produces. The model settles the first for each version of the second. It does not settle which version of the Fed to expect. That is a judgement about the institution, and the results below are reported under both.
How the scenario is built
The nominal policy rate is set 100 basis points above its baseline path in year 2, held there in year 3, and returned to path in year 4. This is imposed. Nothing else is changed by design.
The shock is run twice. In the first run the rate follows the scripted path. In the second a Taylor-type reaction function is live, so the rate responds to the inflation and employment gaps the tightening produces. In that run the rate path after year 2 is solved, not imposed.
Both runs sit on the CBO's published outlook for output, employment, inflation and the funds rate, rendered into a fully articulated economy. The baseline is not a Phylleos forecast. Results are differences from it.
The answer
Percent deviation from the reference path · certified values
The trough arrives in year 3, one year after the rate rise lands and while the policy is still in place. About 30 percent of it is unwound within two years of the reversal. There is no later re-deepening across the remaining twenty-three years of the run.
| Horizon | Fed holds its projected path | Fed responds as it usually does | What the reaction buys |
|---|---|---|---|
| Year 3, the trough | −1.89% | −1.22% | 0.67 pp of trough depth |
| Year 4, rate back on path | −1.44% | −0.78% | 0.66 pp |
| Year 12 | −1.09% | −0.54% | 0.55 pp |
| Peak inflation deviation | −0.21 pp/yr | −0.13 pp/yr | costs 0.08 pp of disinflation |
| Policy rate at the reversal | on path by construction | −69 bp | n/a |
Firms run existing plant less hard for about three years and return to normal intensity. The buildings and equipment not bought during the tightening are not replaced, and the capital stock stays below its reference path through 2050.
Half the permanent loss of the held-rate run. In both runs GDP approaches its reference path from below and does not cross it within the horizon.
What a client receives
The model produces the numbers. The narration layer turns a solved run into a document a board or a policy committee can read, with each figure traceable to the run that produced it.
A 100 basis-point tightening held for one year produces peak disinflation of 0.21 percentage points a year and a contraction that troughs at 1.89 percent of GDP in year 3, one year after the rate rise lands.
With the Fed following its usual reaction function, peak disinflation is 0.13 percentage points and the trough is 1.22 percent of GDP. The rule cuts the policy rate 69 basis points below its projected path at the reversal. By year 12 the two runs sit 1.09 and 0.54 percent below baseline.
What does not come backThe capital stock. Investment forgone during the tightening leaves it 0.80 percent below its reference path through 2050 under the held rate and 0.39 percent under the reacting Fed. GDP approaches its reference path from below in both runs and does not reach it within the horizon.
The fiscal channelHigher rates raise the federal interest bill by about $140 billion in the first year and $261 billion at the peak. That spending is deficit-financed and supports demand, so the contraction is shallower than it would be in a model without the channel. Under the reacting Fed the same channel runs in reverse as the rate falls, which pulls the two runs' long-run outcomes toward each other.
ReliabilityThe timing is the firmest result: a trough one year after the shock, roughly 30 percent unwound within two years of the reversal, and no later re-deepening. This matches the empirical literature on monetary transmission, and the trough depth sits within the range that literature reports. The industry composition of the investment response is a stronger reading than its aggregate level, which rests on a single calibrated parameter.
The fiscal channel
Each year, 0.32 of the gap between the market government-bond rate and the government's average liability rate passes into the interest bill, reflecting the maturity structure of federal debt. Certification confirms the measured passthrough at 0.320 to three digits.
Dollar-billion per year · Fed holds its projected path · certified values
The transfer is deficit-financed and supports demand, which is why it shallows the contraction. It is also the one cost that compounds: it grows with the debt for as long as the run continues.
Limits
From the model documentation.
Your question
Tell us what you have to decide.
Phylleos